Theorem con34b 183

Description: Contraposition. Theorem *4.1 of [WhiteheadRussell] p. 116.

Assertion

Ref	Expression
con34b	|- ((ph -> ps) <-> (-. ps -> -. ph))

Proof of Theorem con34b

Step	Hyp	Ref	Expression
1		con3 110	. 2 |- ((ph -> ps) -> (-. ps -> -. ph))
2		ax-3 6	. 2 |- ((-. ps -> -. ph) -> (ph -> ps))
3	1, 2	impbii 174	1 |- ((ph -> ps) <-> (-. ps -> -. ph))

Syntax hints:  -. wn 2   -> wi 3   <-> wb 163

This theorem is referenced by:  pm4.79 382  notbi 581  imbi1d 675  dfom2 3951  indstr 7630  ntreq0 8984  algcvgblem 13745  evpexun 14322  supnuf 15041  supexr 15043  compfipin0 15436  conss34 16419

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 164

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